Aleskerov F. Mathematics and Democracy: Recent Advances in Voting Systems and Collective Choice

B.: Springer, 2006. - 256p.In this book, different quantitative approaches to the study of electoral systems have been developed: game-theoretic, decision-theoretic, statistical, probabilistic, combinatorial, geometric, and optimization ones. All the authors are prominent scholars from these disciplines. Quantitative approaches offer a powerful tool to detect inconsistencies or poor performance in actual systems. Applications to concrete settings such as EU, American Congress, regional, and committee voting are discussed.Power Indices Taking into Account Agents’ Preferences
The Sunfish Against the Octopus: Opposing Compactness to Gerrymandering
Apportionment: Uni- and Bi-Dimensional
Minimum Total Deviation Apportionments
Comparison of Electoral Systems: Simulative and Game Theoretic Approaches
How to Elect a Representative Committee Using Approval Balloting
On Some Distance Aspects in Social Choice Theory
Algorithms for Biproportional Apportionment
Distance from Consensus: A Theme and Variations
A Strategic Problem in Approval Voting
The Italian Bug: A Flawed Procedure for Bi-Proportional Seat Allocation
Current Issues of Apportionment Methods
A Gentle Majority Clause for the Apportionment of Committee Seats
Allotment According to Preferential Vote: Ecuador’s Elections
Degressively Proportional Methods for the Allotment of the European Parliament Seats Amongst the EU Member States
Hidden Mathematical Structures of Voting
A Comparison of Electoral Formulae for the Faroese Parliament